The present invention relates to the design of adiabatic pulses for MRI (Magnetic Resonance Imaging) and in particular to adiabatic pulses which do not fulfill an adiabatic condition, as defined in a frequency frame.
Magnetic resonance imaging is based on the process of inverting the spins (e.g., of atomic nuclei) which are situated in a strong axial magnetic field and then measuring the electromagnetic radiation of the spins, as the spins return to a more relaxed state. A practical MRI device requires the ability to selectively invert a narrow slice of a subject, in a short period of time and using a low dose of RF radiation. A laboratory frame of reference is customarily defined such that the z axis coincides with the direction of the static magnetic field and the x and y axes are perpendicular thereto. The usual manner of inversion includes applying a z-gradient magnetic field to the subject so that each x-y plane of the subject has a different Larmor frequency and irradiating the subject with a RF radiation pulse, so that only the spins contained in a limited range of Larmor frequencies are inverted. As higher strength magnetic fields are used for MRI imaging, the amount of RF energy absorbed by the body is higher. It is therefore important to limit the amount of radiation to which the subject is exposed. Furthermore, in practical MRI devices, the peak RF amplitude is limited. Usually, there is a tradeoff made between the pulse duration and the RF amplitude.
The relationship between the RF radiation, the magnetic field and the inversion of the spins is governed by the Bloch equations.
When a RF electromagnetic field is applied to a spin which is already in a strong static magnetic field, the RF magnetic field affects the spin. The RF field is very much smaller than the static field, so the RF field is usually described as rotating in the plane perpendicular to the direction of the static magnetic field (the effect of the component in the direction of the static field is negligible). The effect of the RF field on the spins is most conveniently described in a rotating frame of reference, having three perpendicular axes, zxe2x80x2, yxe2x80x2 and xxe2x80x2, known as the xe2x80x9cfrequency framexe2x80x9d or xe2x80x9cFM framexe2x80x9d. The zxe2x80x2 axis is aligned with the main magnetic field denoted by Mz. The xxe2x80x2 axis is, by convention, aligned with the transverse RF field and the yxe2x80x2 axis is perpendicular to both the xxe2x80x2 and zxe2x80x2 axes. The entire frame of reference rotates around the zxe2x80x2 axis at the instantaneous angular frequency of the RF pulse. Both xxe2x80x2 and zxe2x80x2 axes use units of angular frequency, such that all magnetic fields {right arrow over (B)} are represented by vectors xcex3{right arrow over (B)}, where xcex3 is the gyro-magnetic ratio of the spin (type of species thereof). For this reason, magnitudes of magnetic fields are described hereafter in units of angular frequency.
The effective magnetic field to which a spin is subjected as a result of the RF field is preferably defined as a vector in the rotating frame of reference. The magnitude of the zxe2x80x2 component of the vector is equal to the frequency difference between the RF field frequency and the Larmor frequency of the spin. The magnitude of the xxe2x80x2 component is equal to the instantaneous amplitude of the RF field. It should be appreciated that in a uniform zxe2x80x2 directed field, all the spins are located at the same zxe2x80x2 coordinate. When a gradient magnetic field is applied, each spin has a different Larmor frequency and, hence, a different zxe2x80x2 coordinate.
Typically, the net magnetization of a group of spins is treated as a single vector value, called the magnetization vector. Thus, the effect of an inversion pulse is to invert the magnetization vector in a slice of tissue. FIG. 1 is a graph of a typical inverted slice profile. The slice includes an in-slice region, which is inverted by the inversion pulse, an out-of-slice region which is not inverted by the pulse and a transition region in which the post-inversion magnetization varies between +1 (not inverted) and xe2x88x921 (inverted). The magnetization values are normalized to the equilibrium magnetization, M0. For convenience, the in-slice region is usually depicted as centered around the magnetization axis, by defining the off-resonance to be xcexa90=xcfx890xe2x88x92xcfx89c, where xcfx89c is the Larmor frequency at the slice center and xcfx890=xcex3B0 is the Larmor frequency due to the static magnetic field B0. The width of the slice (SW) is usually measured between the two points where the post-inversion (Mz) magnetization is zero. Thus, in FIG. 1xe2x80x94SW/2 is the negative half-slice width, that is measured from the post inversion magnetization (Mz) axis to the point where the slice profile crosses the xcexa90 axis. Similarly, SW/2 is the positive half-slice width, that is measured from the post inversion magnetization (Mz) axis to the point where the slice profile crosses the xcexa90 axis. The slice width is measured in units of frequency. The transition width is defined as twice c0 (half a transition width).
One important type of inversion pulse is an adiabatic pulse. Inversion by an adiabatic pulse is less affected by inhomogenities of the RF field amplitude than are inversions by other types of inversion pulses. An adiabatic pulse uses the following mechanism: An effective field vector of the RF radiation field is initially aligned with the main field magnetization axis (+Mz) direction and its direction is slowly changed until it is aligned in the direction opposite the main field magnetization (xe2x88x92Mz). If the rate of change of the effective field vector is gradual enough, the magnetization vector will track the effective field vector of the RF field and will be inverted when the effective field vector becomes aligned with the xe2x88x92zxe2x80x2 axis. The adiabatic condition (described below) describes the conditions under which the rate of change of the vector is sufficiently gradual to permit tracking. The motion of the effective field vector is characterized by its xe2x80x9ctrajectoryxe2x80x9d, which is the path of the tip of the effective field vector and its xe2x80x9cvelocity profilexe2x80x9d, which describes the instantaneous rate of motion of the effective field vector, along its trajectory.
FIG. 2 is a graph showing the trajectory of a typical adiabatic pulse in the zxe2x80x2-xxe2x80x2 plane. The effective field vector of the pulse starts out at the positive half-slice width SW/2 aligned with the +zxe2x80x2 direction and moves along a half ellipse in the zxe2x80x2-xxe2x80x2 plane until it becomes aligned with the xe2x88x92zxe2x80x2 direction at the negative half-slice width xe2x88x92SW/2. It should be noted that the trajectory shown in FIG. 2 is depicted for spins at the center of the slice. For all other spins, the trajectory shown is effectively shifted along the zxe2x80x2 axis by an amount equal to the difference between the Larmor frequency of the spin and the Larmor frequency at the slice center, i.e., the off-resonance frequency xcexa90. Each point P along the trajectory, defined by a time tP, designates an instantaneous position of the effective field vector, where xcfx891(tP) is the instantaneous RF amplitude and xcex94xcfx89=(xcfx89(tP)xe2x88x92xcfx890) is the difference between the instantaneous RF synthesizer frequency and the Larmor frequency of the spin we are inspecting. As shown in FIG. 2 xcfx891 max is the maximum value of the instantaneous RF amplitude as the point P moves along the trajectory, and X is the projection of the point P on the X-axis whose values are xcfx891, the instantaneous RF amplitude. For each spin which is affected by the adiabatic pulse, a vector connecting the spin and point P is the effective field vector, having a magnitude r. xcex8 is defined as the angle between r and the xxe2x80x2 axis. In order for the rate of change of the vector to be sufficiently gradual to permit tracking, the motion must satisfy the following (adiabatic) condition, xcex93=r/|{dot over (xcex8)}| greater than  greater than 1, where xcex93 is an adiabatic parameter which describes the ratio between r and {dot over (xcex8)}. For the pulse defined by the modulation functions xcfx891 (t) and xcfx89(t), different spins will see different angular velocities. Since r and {dot over (xcex8)} are different for each spin, the adiabatic parameter may ensure tracking for one group of spins but not for another, even at the same point P (at time instance tP) along the trajectory.
As can be appreciated, by increasing {dot over (xcex8)} the RF pulse can be made shorter, however, the adiabatic parameter will become smaller, so tracking may break down and adiabatic tracking may no longer be possible. In many MRI imaging sequences, time is of essence, so a short inversion pulse is desired.
One of the most widely used FM inversion pluses described in the prior art is the sech/tanh pulse. The first term (sech) defines the xxe2x80x2 component of the effective field vector and the second term (tanh) describes the zxe2x80x2 component. The trajectory of the sech/tanh pulse is a half ellipse in the zxe2x80x2-xxe2x80x2 plane:
xe2x80x83xxe2x80x2(t)=A sech(xcex2t)
zxe2x80x2(t)=xcfx89cxe2x88x92B tanh(xcex2t)
where, A=xcex3B1max, B=SW/2, where SW is the inverted bandwidth, t is in the range (xe2x88x92T/2 . . . , T/2) and xcex2=10.6/T (which ensures truncation of the RF amplitude at 1% of its peak value).
xe2x80x9cGeneral Solutions for Tailored Modulation Profiles in Adiabatic Excitationxe2x80x9d, by Thomas E. Skinner and Pierre-Marie L. Robitaille, published in the Journal of Magnetic Resonance 98, pp. 14-23 (1992), describes an inversion pulse having a triangular trajectory.
xe2x80x9cSingle-Shot, B1-Insensitive Slice Selection with a Gradient-Modulated Adiabatic Pulse, BISS-8xe2x80x9d, by Robin A. de Graaf, Klaas Nicolay and Michael Garwood, published in Magnetic Resonance in Medicine 35:652-657 (1996), describes a method for generating an optimal slice-selection pulse, named BISS-8, having an adjustable flip angle.
xe2x80x9cAmplitude- and Frequency-Modulated Pulses to Achieve 90xc2x0 Plane rotations with Inhomogeneous B1 Fieldsxe2x80x9d, by K. Ugurbil, M. Garwood and M. R. Bendall, in Journal of Magnetic Resonance, Vol. 72, pp. 177-185, (1987) and xe2x80x9cAmplitude- and Frequency/Phase-Modulated Refocusing Pulses that Induce Plane Rotations Even in the Presence of Inhomogeneous B1 Fieldsxe2x80x9d, by the same authors, which appeared in the same journal, Vol. 78, pp. 472-497 (1988), described a double rotating reference frame. However these papers do not suggest deviating from the adiabatic condition, as defined in the frequency frame.
It is an object of some embodiments of the present invention to provide adiabatic inversion or excitation pulses which seemingly violate the adiabatic condition (hereafter the xe2x80x9cfrequency-frame adiabatic conditionxe2x80x9d), namely that r/|{dot over (xcex8)}| greater than  greater than 1, as defined in the frequency frame.
The adiabatic condition may be generally stated as: a magnetization vector will track an effective field vector if the rate of precession of the magnetization vector about the effective field vector is much faster than the angular velocity of the effective field vector. For RF pulses that fulfill the requirements of the adiabatic condition, the Bloch equations can be approximately solved, at least to the extent of determining the end magnetization vector, since, if the effective field vector varies slowly enough, the magnetization vector will track the effective field vector. If the path of the effective field vector is known, the path of the magnetization vector and its end value can also be known. Thus, an important feature of adiabatic pulses is that the magnetization vector has only a small angle subtended between itself and the effective field vector. Hence, the term, xe2x80x9ctrackingxe2x80x9d. In the prior art, the reference frame in which the adiabatic condition was studied was the frequency reference frame, which rotates at the instantaneous frequency of the FM pulse.
The inventors have discovered useful formulations for the adiabatic condition in reference frames other than the frequency frame. Thus, a RF pulse can be adiabatic even if it violates the above frequency-frame adiabatic condition, providing that it complies with an adiabatic condition in a different reference frame. The inventors have also discovered a family of such reference frames, where defining the adiabatic condition is straight forward, and in which useful adiabatic RF pulses may be defined. A second order adiabatic condition, as one example of a different adiabatic condition, is defined by analyzing the adiabatic condition in a double-rotating reference frame, in which the effective field vector performs a composite rotation consisting of both (a) the instantaneous frequency of the FM pulse and (b) the motion of the tip of effective field vector (in the frequency frame). A third-order adiabatic condition can be defined using a triple-rotating reference frame, etc.
In accordance with a preferred embodiment of the invention, it is realized that it is profitable to search for additional reference frames in which the adiabatic condition may be fulfilled. Each new reference frame discovered may be used to define adiabatic RF pulses, which would not be considered to be adiabatic in the frequency reference frame. Moreover, if a RF pulse is adiabatic in any reference frame, can be denoted as xe2x80x9cadiabaticxe2x80x9d.
The following definitions should be clearly differentiated, and are not always differentiated in the current state of the art:
(a) Adiabatic pulses are pulses in which the magnetization vector closely tracks (typically  less than 21xc2x0) an effective field vector of the pulse, for at least a portion of the spins in the irradiated sample and for substantially the entire trajectory.
(b) FM pulses are pulses in which the frequency of the applied RF field is modulated.
(c) B1-insensitive pulses are pulses that have a similar final effect (typically inversion or excitation) on a certain set of spins, even if the amplitude of the B1 field is not the same for all the spins.
In the past, the distinction between these types of pulses were sometimes confused. A particular case in point is the sech/tanh pulse. One of the important qualities of this pulse is that it is relatively insensitive to B1 inhomogenities, as long as the RF amplitude exceeds a certain threshold value. In addition, it appears to work by an adiabatic mechanism. However, the inventors have noted that during the application of this pulse, especially at threshold conditions (discussed below), an angle of over 40xc2x0 may be subtended between the effective field vector of the pulse and the magnetization vector. Thus, at least in some of the cases where the sech/tanh pulse works, it cannot be considered adiabatic (in the frequency frame).
It should be appreciated that there should be no apriori expectation that the sech/tanh pulse works by an adiabatic mechanism, since the sech/tanh pulse is an analytical solution of the Bloch equations. Nevertheless, it is generally accepted in the art that the sech/tanh pulse is an adiabatic pulse.
The adiabatic condition as defined in the frequency frame, imposes a strict limitation on the maximum angular velocity of the effective field vector, as a function of the size of the field vector. In accordance with a preferred embodiment of the present invention, a family of reference frames is defined, in which the limitation of maximum velocity is replaced by less strict limitations. The family of reference frames is defined as a series of reference frames, each having a less strict limitation than a preceding one. Further, a property of this family of reference frames is the ease in which they can be related to the frequency and laboratory frames of reference. Thus, pulses defined in a reference frame of this family can be easily described in the frequency frame. Further, it is also straightforward to compare a pulse that is adiabatic in one of these frames of reference to a known pulse in the frequency frame.
Another property of this family of reference frames is that under certain boundary conditions, such a reference frame can be collapsed to the frequency frame. Thus, any pulse that is adiabatic in the frequency frame will be adiabatic in any of reference frames of the family. As a direct consequence, it is assured that it is possible to generate an adiabatic pulse in one of these reference frames, which is at least as fast as a comparable pulse in the frequency frame.
In accordance with a preferred embodiment of the invention, the series of reference frames are defined such that each reference frame takes into account the effect of the rotation of the effective field vector of the previous reference frame in the series. The first reference frame in the family series is the double rotating reference frame, which takes into account the rotation of the effective field vector of the frequency frame. The inventors have determined that in a double-rotating frame of reference (described below) the sech/tanh pulse is adiabatic. The limitation that is relaxed in the double-rotating frame of reference is the limitation of maximum angular velocity. Instead, only the maximum angular acceleration is directly limited. However, the boundary requirements may impose some velocity limitation. For example, a pulse having known starting and ending angular velocities and a limited duration, will also have a limited maximum velocity determined by the maximum allowed acceleration.
It should be appreciated that the form of the adiabatic condition itself is not changed by moving into a different frame of reference. Rather, what is changed is the pulse designer""s representation of the adiabatic condition.
It is an object of another aspect of the present invention to provide an optimization method in which RF pulses are not restricted by the frequency frame adiabatic condition.
It is an object of yet another aspect of the present invention to provide a pulse generation method that generates pulses which are not restricted by the frequency frame adiabatic condition.
It is also an object of some aspects of the present invention to provide a method of tipping spins by an angle, which method uses an adiabatic inversion pulse which is not restricted by the frequency frame adiabatic condition. A most useful tip angle is 180xc2x0, however, other tip angles are also preferably achieved using methods of the present invention. Such tip angles may be achieved using a single pulse or by using a pulse comprised of several segments.
In a preferred embodiment of the invention, the reference frame for defining the adiabatic condition is the double rotating reference frame (described below). When changing from the frequency frame to the double-rotating reference frame, a field that has a magnitude of the rotation velocity and a direction aligned with the rotation axis, is added. The effective field vector of the pulse in a double rotating frame of reference includes the effect of a second virtual field, additive to the first virtual field of the frequency frame, and has a magnitude rxe2x80x2={square root over ({dot over (xcex8)})}2+r2. Thus, the larger {dot over (xcex8)} the greater the difference between the frequency-frame effective field vector and the double-rotating effective field vector. An angle xcfx86 is defined as extending between the frequency frame effective field vector and the double-rotating effective field vector, tan((xcfx86)={dot over (xcex8)}/r. When {dot over (xcex8)} is relatively (to r) small, xcfx86 will be small and the two effective field vectors will be substantially aligned. However, in the double-rotating reference frame the adiabatic condition does not directly limit {dot over (xcex8)}, so xcfx86 can be very large.
A second order adiabatic pulse works by ensuring tracking between the net magnetization vector of the spins and the double-rotating effective field vector. The second order adiabatic condition requires that the double rotating effective field vector move slowly, i.e., xcex932=rxe2x80x2/|{dot over (xcfx86)}| greater than  greater than 1.
It should be noted that in order to construct a practical adiabatic pulse, additional limitations may apply. For example, in an inversion pulse, the initial and ending {dot over (xcex8)} are typically zero, the initial xcex8 is zero and the end xcex8 is 180xc2x0 (or xe2x88x9290xc2x0 and 90xc2x0). In addition, there is usually a limitation on available RF amplitude.
It should be appreciated that by relaxing the requirement of adiabaticity, many optimization methods and pulse generation methods which are known in the art can be modified and applied to generate new pulses and families of pulses, using the new adiabatic conditions rather than the frequency frame adiabatic condition.
In a preferred embodiment of the invention, when an adiabatic condition is used as a constraint in a numerical optimization technique, an adiabatic condition other than a frequency frame adiabatic condition is used, for example, a second order adiabatic condition.
In a preferred embodiment of the invention, a pulse is generated using an optimization technique, whereby the adiabatic constraint is defined for different frames of reference for different portions of the pulse.
In a preferred embodiment of the invention, the rate of motion along the trajectory of a pulse is determined responsive to a maximum rate of motion that satisfies the adiabatic condition for all the spins in the slice for each point P along the trajectory.
Preferably, an optimal velocity profile is determined and then scaled to obtain a shortest pulse that still performs the desired action, such as inversion. Alternatively or additionally, the rate of motion along the trajectory is optimized numerically or otherwise.
In a preferred embodiment of the invention, the maximum rate of motion is determined for a mathematical support region that defines which portions of a sample should be inverted (in-slice) and which not (out-of-slice). This definition is preferably by way of ranges of Larmor frequencies, which translate to a z coordinate, in a z-gradient type magnetic field. Alternatively or additionally, the support region includes a range of expected local RF field strengths, such that the pulse can be verified as adiabatic for the expected RF range. Typically, the support regions will be rectangular (Larmor frequency range by RF amplitude range). In a preferred embodiment of the invention, the support regions are non-rectangular.
In a preferred embodiment of the invention, the trajectory is divided into a plurality of segments and the maximum allowed rate of motion is calculated successively for each such segment, preferably starting at the beginning of the pulse. In a preferred embodiment of the invention, the maximum rate of motion for each point in the support region is calculated by determining the smallest time of travel for a segment lying between two points on the trajectory, the travel time of which will still maintain the adiabatic condition. Thereafter, the largest of these times is used in the final pulse, for that segment of the trajectory. In some cases the entire pulse profile is scaled.
Another aspect of the present invention relates to excitation pulses, i.e. flipping a magnetization vector of the spins by xcfx80/2 radians, using a different physical principle from that used in the prior art. Prior art adiabatic excitation pulses align the magnetization vector with the xxe2x80x2 axis. This alignment is achieved by having the magnetization vector of the spins lock to the effective field vector of the pulse and then steering the field vector of the pulse to be aligned with the xxe2x80x2 axis. This is not the method of some embodiments of the present invention.
In accordance with a preferred embodiment of the present invention, the angular velocity ({dot over (xcex8)}) is increased, thereby increasing xcfx86. When xcfx86 approaches 90 degrees, the pulse is stopped. The effective field vector of the pulse is in the zxe2x80x2-xxe2x80x2 plane, so, being perpendicular thereto, the net magnetization vector of the spins is substantially aligned with the yxe2x80x2 axis. As the yxe2x80x2 axis is perpendicular to the zxe2x80x2 axis, the magnetization vector is deemed excited. Preferably, the velocity profile of the excitation pulse is found using the support region method of pulse generation, described herein. Additionally or alternatively, r is reduced, preferably once a sufficiently high {dot over (xcex8)} is achieved, thereby also increasing xcfx86.
An inversion pulse in accordance with another preferred embodiment of the invention is a 3xcfx80 inversion pulse, in which the magnetization vector completes more than one circuit in the zxe2x80x2-xxe2x80x2 plane. Optionally, higher angle inversion pulses may be used, such as 5xcfx80 or 7xcfx80. One advantage of such pulses is that very high angular velocities of the effective field vector and the magnetization vector may be achieved. Such high rotation pulses may also be used to tip spins by other angles, such as 90xc2x0 or any other angle.
A tipping pulse, in accordance with another preferred embodiment of the invention, has a minimum adiabatic parameter that is lower than for a comparable sech/tanh pulse. A comparable sech/tanh pulse may be defined as having a similar peak RF amplitude, a ratio of between 0.1 and 3 between the RF amplitude and the half slicewidth and a similar duration.
An aspect of some preferred embodiments of the invention relates to a method of generating high-order adiabatic pulses by conveying first-order adiabatic pulses into a higher-order frame. In one example, a sech/tanh pulse is used to define a trajectory in a second-order frame. Preferably, the conveyed sech/tanh may be used for frequency selective excitation and/or saturation.
An aspect of some preferred embodiments of the invention relates to a pulse having a linear phase between RF amplitude and excitation phase. Preferably, such a pulse comprises a sech/tanh which is conveyed to a second order frequency frame. In a preferred embodiment of the invention, such a pulse is used to map magnetic susceptibility of a body.
An aspect of some preferred embodiments of the invention relates to an adiabatic pulse having a linear relationship between an excitation phase and off-resonance frequencies. In a preferred embodiment of the invention, such a pulse is used for excitation. Alternatively or additionally, such a pulse is used for refocusing.
An aspect of some preferred embodiments of the invention relates to a method of generating pulses comprising multiplying the defining functions of an existing pulse by modification functions, possibly exponential functions, thereby defining a new pulse trajectory. In a preferred embodiment of the invention, the pulse is a sin/cos or a sech/tanh pulse which is multiplied by an exponentially decreasing function.
An aspect of some preferred embodiments of the invention relates to spiral trajectory pulses, in which the radius of the trajectory is inversely related to its angular velocity. In a preferred embodiment of the invention, such a pulse is generated by multiplying the defining function of a known pulse, such as a sin/cos pulse by exponential functions. Alternatively or additionally, such a pulse is generated by selecting functions for r and {dot over (xcex8)} which vary from 1 to 0 and from 0 to 1, respectively. Alternatively or additionally, to selecting Cartesian functions for defining the pulse, polar coordinate functions may be used. Alternatively, a different coordinate notation may be used. In a preferred embodiment of the invention, the spiral is an inward spiral, whereby the angular velocity increases as the radius decreases. Preferably, such a pulse is used to tip a magnetization vector out of an Xxe2x80x2Zxe2x80x2 plane and near to a Yxe2x80x2 axis (in a frequency frame) (i.e., excitation). Such tipping usually utilizes an increasing {dot over (xcex8)}, with a decreasing or an increasing radius. Alternatively, such a pulse is used for inversion, for example by having the pulse advance along the trajectory until a 90 degree angle (of the effective magnetization or the material magnetization with the Mz direction) is achieved (in the frequency frame) and then reversing the trajectory (or using a reversed trajectory of a different pulse) to complete another 90 degrees of tipping. Alternatively, the spiral is an outward spiral, which starts with a small radius, which increases.
Alternatively or additionally, the spiral is wavy, for example if the functions which vary from 0 to 1 (and 1 to 0) are not monotonic. Alternatively or additionally, only a portion of a spiral is achieved. These spiral trajectories may be visualized in the double rotating frequency frame as trajectories that start at a first radius r and a first {dot over (xcex8)} and end at a second radius and a second {dot over (xcex8)}. In general some of the contemplated trajectories have the property that their first-order adiabatic parameter decreases between their start to their end, for example, if the ending radius is smaller and the ending angular velocity is higher.
In some preferred embodiments of the invention, pulses generated by methods described herein and pulses described herein are B1 insensitive. Pulses as described herein are preferably incorporated into an MRI device, an NMR device, or an NM spectroscopy device. A typical MRI device, suitable to be programmed to radiate such RF pulses, preferably includes a static Z directed main magnetic field, x, y and z gradient coils which apply gradients to the main magnetic field and an RF transmitter which transmits the pulse. Preferably, the RF transmitter is controlled by an RF synthesizer which converts the pulse parameters into RF signals. Preferably the synthesizer can modulate amplitude, phase and/or frequency.
There is thus provided in accordance with a preferred embodiment of the invention, a method of generating an adiabatic FM pulse, comprising:
selecting a starting trajectory for the pulse; and
determining a velocity profile along the trajectory by constraining at least a portion of the velocity profile to fulfill a given adiabatic condition other than a frequency frame adiabatic condition.
Preferably, the given adiabatic condition is an adiabatic condition defined in a double rotating frame of reference. Alternatively or additionally, at least a second portion of the velocity profile is constrained to fulfill a different adiabatic condition from said given adiabatic condition. Alternatively or additionally, said FM pulse is analytically described. Alternatively or additionally, an adiabatic parameter is maintained at a minimum value which ensures tracking for a predefined support region of the spins, for substantially the entire trajectory.
Preferably, said minimum value ensures tracking in a double rotating reference frame. Alternatively or additionally, the minimum value is determined based on an expected range of RF field inhomogenities at the spins. Alternatively or additionally, the minimum value is determined based on a desired slice profile.
In a preferred embodiment of the invention, the method comprises:
for each point in the support region, determining a shortest time to advance along a particular segment of the trajectory; and
selecting the longest such time as the time to advance along the trajectory in the determined velocity profile.
Preferably, said selected trajectory is used to generate said generated pulse. Alternatively or additionally, the method comprises:
calculating new pulse parameters for each of said points, using said selected longest time; and
repeating said determining a shortest time, for consecutive segments along the trajectory, utilizing said calculated new pulse parameters. Preferably, said new pulse parameters comprise a velocity profile of the pulse for each point of the support region.
There is also provided in accordance with a preferred embodiment of the invention, a method of generating an FM pulse, to meet certain conditions, comprising:
providing an original FM pulse and desired conditions for operation thereof, and
optimizing said original pulse to generate said generated FM pulse, while constraining said pulse to fulfill a given adiabatic condition other than a frequency-frame adiabatic condition, over at least a portion thereof.
Preferably, said given adiabatic condition is a second order adiabatic condition.
In a preferred embodiment of the invention, said generated pulse does not fulfill a first order adiabatic condition over most of said constrained portion.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an adiabatic pulse, comprising:
selecting a frequency-frame adiabatic pulse, having a trajectory and a velocity profile;
defining a new pulse having a new trajectory and a new velocity profile, in a different frame of reference, wherein at least a portion of the trajectory is substantially copied from the frequency-frame to the different frame of reference.
Preferably, at least a portion of the velocity profile is substantially copied from the frequency-frame to the different frame of reference.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an adiabatic pulse, comprising:
selecting a frequency-frame adiabatic pulse, having a trajectory and a velocity profile;
defining a new pulse having a new trajectory and a new velocity profile, in a different frame of reference, wherein at least a portion of the velocity profile is substantially copied from the frequency-frame to the different frame of reference.
In a preferred embodiment of the invention, said adiabatic pulse comprises an adiabatic sech/tanh pulse.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an adiabatic pulse, comprising:
providing a sech/tanh pulse, having a trajectory and a velocity profile;
defining a new pulse having a new trajectory and a new velocity profile, in a different frame of reference, wherein at least a portion of the velocity profile and at least a portion of the trajectory are substantially copied from the frequency-frame to the different frame of reference.
In a preferred embodiment of the invention, said adiabatic pulse comprises a cos/sin pulse.
In a preferred embodiment of the invention, said generated pulse is an excitation pulse which excites irradiated material. Preferably, said excitation pulse generates an effective magnetization vector in said frequency frame and wherein a magnetic vector of a material being irradiated by said pulse does not track said effective magnetization vector. Alternatively or additionally, said excitation pulse generates an excitation with a linear phase dependency between an off-resonance and a phase of said excitation. Alternatively or additionally, said excitation comprises frequency-selective excitation.
In a preferred embodiment of the invention, said generated pulse is an inversion pulse. Preferably, said inversion pulse comprises a frequency-selective inversion pulse.
In a preferred embodiment of the invention, said different frame of reference is a double-rotating frame of reference. Alternatively or additionally, said trajectory is a half-ellipse trajectory. Alternatively or additionally, said pulse is an analytical solution of a Bloch equation.
In a preferred embodiment of the invention, the method comprises setting boundary conditions for the defined pulse. Alternatively or additionally, a time scale of at least a portion of the velocity profile is changed for the different frame of reference.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an MR pulse, comprising:
selecting a start radius and an end radius for a trajectory of a pulse in a higher than first-order reference frame, wherein said start radius is greater than said end radius, wherein said radius changes between said start radius and said end radius along said trajectory; and
defining a velocity profile along said trajectory, such that an angular velocity in a frequency frame is higher at the end than at the beginning of said trajectory, wherein said angular velocity changes along said trajectory. Preferably, said higher than first-order reference frame is a second-order reference frame. Alternatively or additionally, said pulse is constrained to be adiabatic over a significant portion of said trajectory. Alternatively or additionally, said end radius is less than 50% of said start radius. Alternatively or additionally, said end radius is less than 40% of said start radius. Alternatively or additionally, said end radius is less than 20% of said start radius. Alternatively or additionally, said end radius is less than 10% of said start radius. Alternatively or additionally, said end radius is less than 5% of said start radius. Alternatively or additionally, said angular velocity is at least twice as large at said end than at said start. Alternatively or additionally, said angular velocity is at least ten times as large at said end than at said start. Alternatively or additionally, said change in radius is monotonic.
Alternatively, said change in radius is not monotonic.
In a preferred embodiment of the invention, said change in angular velocity is monotonic. Alternatively, said change in angular velocity is not monotonic.
In a preferred embodiment of the invention, said pulse is time-reversed, to start with a small radius and large angular velocity and end with a large radius and small angular velocity. Alternatively or additionally, said pulse defines a substantially spiral trajectory in a frequency frame, wherein said trajectory circles a plurality of times around an origin location of said frequency frame. Alternatively or additionally, said end radius and said end angular velocity are selected such that the pulse excites an irradiated material. Alternatively or additionally, the method comprises attaching a time reversed pulse to said pulse, to produce a complete pulse, wherein said time-revered pulse is a time-reversed version of pulse which tips a magnetization vector to have a significant transverse magnetization. Preferably, said time reversed pulse comprises a time-reversed version of said generated pulse. Alternatively, said time reversed pulse comprises a time-reversed version of a pulse other than said generated pulse.
In a preferred embodiment of the invention, said end point and said reversed pulse are selected so that the complete pulse will effect an inversion of an irradiated material.
In a preferred embodiment of the invention, said trajectory is defined in Cartesian notation by:
selecting a first function for defining a first component of said pulse; and
selecting a second function for defining a second component of said pulse,
wherein said first and said functions vary responsive to the value of a parameter.
Preferably, at least one of said functions comprises a function of a power of said parameter.
In a preferred embodiment of the invention, said trajectory is generated by multiplying each of a pair of component functions of an existing trajectory by a time-varying function.
Preferably, said time-varying function comprises an exponential relationship, for at least one of said component functions.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an MR pulse, comprising:
selecting a start radius and an end radius, for a trajectory of a pulse, in a higher than first-order reference frame, wherein said end radius is greater than said start radius; and
defining a velocity profile along said trajectory, such that an angular velocity in a frequency frame is higher at the end than at the beginning of said trajectory and such that a frequency frame adiabatic condition is not maintained at said end of said pulse.
In a preferred embodiment of the invention, the method comprises numerically optimizing the generated pulse. Preferably, numerically optimizing comprises optimizing said velocity profile. Alternatively or additionally, numerically optimizing comprises optimizing said selected trajectory.
There is also provided in accordance with a preferred embodiment of the invention, a pulse generated by the above described methods and an MRI device which applies such a pulse.
There is also provided in accordance with a preferred embodiment of the invention, a method of MRI imaging, comprising:
providing a patient to be imaged; and
applying a pulse, as described above, to at least a portion of the patient.
There is also provided in accordance with a preferred embodiment of the invention, a method of inverting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse having a minimum adiabatic parameter value of less than 1.4 over at least 1% of the duration of the pulse.
Preferably, the minimum value is less than 1.2. Alternatively, the minimum value is less than 0.5. Alternatively or additionally, the minimum value is less than 0.1.
In a preferred embodiment of the invention, said FM pulse is adiabatic. Alternatively or additionally, said adiabatic parameter value is below said value for at least 5% of the duration of the pulse. Alternatively or additionally, said adiabatic parameter value is below said value for at least 10% of the duration of the pulse. Alternatively or additionally, said adiabatic parameter value is below said value for at least 20% of the duration of the pulse.
There is also provided in accordance with a preferred embodiment of the invention, a method of inverting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse having a duration, a peak RF amplitude, a ratio between half a bandwidth of the pulse and the RF amplitude and a minimum adiabatic parameter value of less than 0.9 of the minimum value possible with a sech/tanh pulse having said duration, said peak RF amplitude and said ratio. Preferably, said ratio is between 0.1 and 3. Alternatively or additionally, said ratio is between 1 and 10. Alternatively or additionally, said sech/tanh pulse is B1-insensitive over a scale of 1:2. Alternatively or additionally, said FM pulse is adiabatic.
There is also provided in accordance with a preferred embodiment of the invention, a method of inverting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse having an average adiabatic parameter value of less than 3, over the duration of the pulse.
Preferably, said FM pulse is adiabatic. Alternatively or additionally, the average value is less than 2. Alternatively or additionally, the average value is less than 1.5. Alternatively or additionally, the average value is less than 1. Alternatively or additionally, the average value is less than 0.5.
There is also provided in accordance with a preferred embodiment of the invention, a method of inverting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse having a trajectory, wherein said FM pulse does not fulfill a frequency-frame adiabatic condition along at least 20% of said trajectory, wherein at least 50% of said trajectory, in a frequency-frame of reference which rotates at the instantaneous frequency of the RF pulse, is outside a trajectory defined by sinxcex1/cosxcex1, wherein, xcex1 less than 0.9. Alternatively or additionally, xcex1 less than 0.7. Alternatively or additionally, xcex1 less than 0.4. Alternatively or additionally, at least 50% comprises at least 70%. Alternatively or additionally, at least 20% comprises at least 40%.
There is also provided in accordance with a preferred embodiment of the invention, a method of exciting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field;
irradiating the spins with an FM RF pulse, wherein said RF pulse, in a zxe2x80x3-xxe2x80x3 double rotating frame of reference which rotates at the instantaneous angular velocity of the RF pulse and at the frequency of the RF pulse, has an effective magnetic field vector with an angle phi between the effective field vector and the zxe2x80x3 axis of the frame; and
discontinuing said irradiation when said angle phi is in the vicinity of 90xc2x0. Preferably, said FM pulse is adiabatic.
There is also provided in accordance with a preferred embodiment of the invention, a method of exciting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field;
irradiating the spins with an FM RF pulse, wherein said RF pulse, in a zxe2x80x3-xxe2x80x3 double rotating frame of reference which rotates at the instantaneous angular velocity of the RF pulse and at the frequency of the RF pulse, has an effective magnetic field vector with an angle phixe2x80x3 between a net magnetization of the sample and the zxe2x80x3 axis of the frame; and
discontinuing said irradiation when said angle phixe2x80x3 is in the vicinity of 90xc2x0.
In a preferred embodiment of the invention, said pulse is an adiabatic pulse. Preferably, said pulse is a second order adiabatic pulse. Alternatively or additionally, said pulse comprises a pulse, substantially half of whose trajectory is defined by a sech/tanh relationship.
There is also provided in accordance with a preferred embodiment of the invention, a method of tipping spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse having a velocity profile and a trajectory in a frequency frame, wherein said RF pulse fulfills an adiabatic condition over a substantial portion thereof, which adiabatic condition is different from a frequency frame adiabatic condition, wherein said trajectory has an angular extent of over xcfx80 and wherein said angular velocity is maintained at more than 5% of a maximum angular velocity for the entire pulse excluding a beginning and end thereof.
Preferably, said FM pulse is adiabatic. Alternatively or additionally, said angular extent is over 2xcfx80. Alternatively or additionally, said angular extent is over 3xcfx80. Alternatively or additionally, said angular extent is over 4xcfx80.
There is also provided in accordance with a preferred embodiment of the invention, a method of affecting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse, wherein said RF pulse, in a zxe2x80x3-xxe2x80x3 double rotating frame of reference which rotates at the instantaneous angular velocity of the RF pulse and at the frequency of the RF pulse, has a trajectory which comprises at least 10% of an ellipse.
Preferably, said FM pulse is adiabatic. Alternatively or additionally, the trajectory comprises at least 15% of an ellipse. Alternatively or additionally, the trajectory comprises approximately 25% of an ellipse.
There is also provided in accordance with a preferred embodiment of the invention, a method of affecting spins for magnetic resonance imaging, comprising:
subjecting the spins to a strong magnetic field; and
irradiating the spins with an FM RF pulse, wherein said RF pulse, in a zxe2x80x3-yxe2x80x3-xxe2x80x3 double rotating frame of reference which rotates at the instantaneous angular velocity of the RF pulse and at the frequency of the RF pulse, wherein said yxe2x80x3 axis is aligned with a frequency frame yxe2x80x2 axis and wherein said zxe2x80x3 axis is aligned with a frequency frame effective field vector of the pulse, wherein said pulse has a trajectory which starts at approximately yxe2x80x2=0 and ends at approximately zxe2x80x2=0.
Preferably, said FM pulse is adiabatic. Alternatively or additionally, said trajectory is a quarter ellipse. Alternatively, said trajectory is substantially a straight line. Alternatively said trajectory is substantially a quarter of a rectangle.